Hi Danielle,
As you write, oversize and burnt are each challenges for rehousing. Both together are doubly so! It would be helpful to know if the charring is even across the surface or if there are areas that are less affected and more structurally stable. Ideally it would be great to be able to support the piece adequately while minimizing surface contact with charred surfaces but that may not be possible if it was extensively burned. At first guess I would be inclined to look at the slick side of soft Tyvek wrap or Teflon (PTFE) "Relic Wrap"
There are some other materials that might be useful listed on this page https://spnhc.org/rehousing-materials/ excerpted from the rehousing chapter in the AIC/SPNHC Preventive Conservation Collection Storage book.
Are you able to share a picture with the group? That might facilitate some additional brainstorming.
------------------------------
Rachael Arenstein
A.M. Art Conservation, LLC
rachael@amartconservation.com------------------------------